Can I use a programming language other than C, C++, or Java for the contest?

No. Allowing additional languages would cause more work for the Site Directors (who must install the necessary software) and the Regional Chief Judges (who must write judging utilities for the language). Also, there is a fairness issue: programs written in scripting languages like Perl and very high level languages like Haskell are often an order of magnitude shorter than programs written in traditional languages.

Does it matter which language I use?

Contest problems are designed with C++ and Java programmers in mind, so C programmers may be at a disadvantage. C++ and Java are roughly comparable, so pick whichever one you're most familiar with.